Question: Simplify the following expression: $x = \dfrac{-3k^2 + 9k + 54}{k + 3} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-3$ , so we can rewrite the expression: $ x =\dfrac{-3(k^2 - 3k - 18)}{k + 3} $ Then we factor the remaining polynomial: $k^2 {-3}k {-18} $ ${3} {-6} = {-3}$ ${3} \times {-6} = {-18}$ $ (k + {3}) (k {-6}) $ This gives us a factored expression: $\dfrac{-3(k + {3}) (k {-6})}{k + 3}$ We can divide the numerator and denominator by $(k - 3)$ on condition that $k \neq -3$ Therefore $x = -3(k - 6); k \neq -3$